Predicting ADHD from Resting-State fMRI

In this project, we work on resting-state fMRI data to investigate brain connectivity patterns.

# Import necessary libraries
import os
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from nilearn import datasets, maskers, plotting
from nilearn.input_data import NiftiLabelsMasker
from nilearn.connectome import ConnectivityMeasure


# Ignore warnings for cleaner output
import warnings
warnings.filterwarnings('ignore')

c:\Users\lacom\anaconda3\lib\site-packages\nilearn\input_data\__init__.py:23: FutureWarning: The import path 'nilearn.input_data' is deprecated in version 0.9. Importing from 'nilearn.input_data' will be possible at least until release 0.13.0. Please import from 'nilearn.maskers' instead.
  warnings.warn(message, FutureWarning)

• This section imports the necessary Python libraries for various tasks:
  • os: This module provides a portable way of using operating system-dependent functionality.
  • pandas as pd: Pandas is a powerful data manipulation library. It's commonly imported as pd for brevity.
  • numpy as np: NumPy is a library for numerical computing in Python. It's often imported as np for brevity.
  • matplotlib.pyplot as plt: Matplotlib is a plotting library for Python. The pyplot module provides a MATLAB-like interface for plotting.
  • seaborn as sns: Seaborn is a statistical data visualization library based on Matplotlib. It provides a high-level interface for drawing attractive and informative statistical graphics.
  • nilearn.datasets: Nilearn is a Python module for fast and easy statistical learning on neuroimaging data. It provides datasets and tools specifically tailored for neuroimaging analysis.
  • nilearn.maskers: This submodule contains tools for extracting data from neuroimaging data formats.
  • nilearn.plotting: This submodule provides functions to plot various neuroimaging data.
  • NiftiLabelsMasker: This class in Nilearn is used to extract time series from regions defined by labels in a Nifti image.
  • ConnectivityMeasure: This class in Nilearn is used to compute connectivity matrices from neuroimaging data.

data = datasets.fetch_adhd(n_subjects=None, data_dir=None, url=None, resume=True, verbose=1)

This line of code is using the fetch_adhd function from the datasets module in the nilearn library to download the ADHD dataset. Let's break down the parameters used in this function:

• n_subjects: This parameter specifies the number of subjects to fetch from the dataset. When set to None, it fetches all available subjects.
• data_dir: This parameter specifies the directory where the data will be stored. When set to None, it uses the default data directory.
• url: This parameter specifies the URL from which to download the dataset. When set to None, it uses the default URL.
• resume: This parameter determines whether to resume downloading if a partial download exists. When set to True, it resumes the download if it was interrupted.
• verbose: This parameter controls the verbosity of the output during the download process. When set to 1, it displays progress information during the download.

Once executed, this line will download the ADHD dataset and store it in the specified directory (or the default directory if none is provided). It will fetch all available subjects in the dataset. Additionally, it will display progress information during the download process.

# Get the keys

print('Keys:',list(data.keys()))

# Get the number of subjects

print('Number of subjects:', len(data.func))

Keys: ['func', 'confounds', 'phenotypic', 'description']
Number of subjects: 40

data.description

"ADHD 200\n\n\nNotes\n-----\nPart of the 1000 Functional Connectome Project. Phenotypic\ninformation includes: diagnostic status, dimensional ADHD symptom measures,\nage, sex, intelligence quotient (IQ) and lifetime medication status.\nPreliminary quality control assessments (usable vs. questionable) based upon\nvisual timeseries inspection are included for all resting state fMRI scans.\n\nIncludes preprocessed data from 40 participants.\n\nProject was coordinated by Michael P. Milham.\n\nContent\n-------\n    :'func': Nifti images of the resting-state data\n    :'phenotypic': Explanations of preprocessing steps\n    :'confounds': CSV files containing the nuisance variables\n\nReferences\n----------\nFor more information about this dataset's structure:\nhttp://fcon_1000.projects.nitrc.org/indi/adhd200/index.html\n\nLicence: usage is unrestricted for non-commercial research purposes.\n"

The data.description provides detailed information about the ADHD dataset.

• Dataset Name: ADHD 200

• Notes:

  • This dataset is part of the 1000 Functional Connectome Project.
  • Phenotypic information includes diagnostic status, dimensional ADHD symptom measures, age, sex, intelligence quotient (IQ), and lifetime medication status.
  • Preliminary quality control assessments (usable vs. questionable) based on visual timeseries inspection are included for all resting-state fMRI scans.
  • It includes preprocessed data from 40 participants.
  • The project was coordinated by Michael P. Milham.

• Content:

  • 'func': Nifti images of the resting-state data.
  • 'phenotypic': Explanations of preprocessing steps.
  • 'confounds': CSV files containing the nuisance variables.

• References:

  • For more information about the dataset's structure, a reference link is provided: ADHD 200 Dataset Structure.

• License:

  • Usage is unrestricted for non-commercial research purposes.

Explore the Target Variable (Y)

# Let's load the phenotype data

pheno = pd.DataFrame(data.phenotypic)

This line of code loads the phenotype data from the ADHD dataset into a Pandas DataFrame named pheno.

• Loading Phenotype Data:

  • data.phenotypic: This accesses the phenotypic data from the data object, which is assumed to be a dictionary-like object containing various components of the ADHD dataset, including the phenotype information.

  • pd.DataFrame(): This function from the Pandas library converts the phenotypic data into a DataFrame, a two-dimensional labeled data structure with columns of potentially different types.

  • pheno: This variable is assigned to hold the DataFrame containing the phenotype data.

After executing this line, the pheno DataFrame will contain the phenotype information from the ADHD dataset, with each row representing a subject and each column representing a specific phenotypic variable (e.g., diagnostic status, ADHD symptom measures, age, sex, IQ, medication status).

# INFO

df = pheno

# Display the shape of the data
print("Data Shape:")
print(df.shape)

# Check for any duplicate entries in the data.
print('')
print("Duplicate Values:")
print('(',df.duplicated().sum(),')')


# Display the data types of the columns
print("\nData Types:")
print(df.dtypes.value_counts())

# Check for missing values
missing_columns = df.columns[df.isnull().any()]
if missing_columns.size > 0:
    missing_values = df[missing_columns].isnull().sum()
    missing_percentage = (missing_values / len(df)) * 100

    # Combine missing_values and missing_percentage into a single DataFrame
    missing_data = pd.concat([missing_values, missing_percentage], axis=1, keys=['Total', 'Percent'])

    # Sort the missing_data DataFrame by Total column in descending order
    missing_data = missing_data.sort_values(by='Total', ascending=False)

    # Print missing data
    print("\nMissing Data:")
    print(missing_data.to_string())
else:
    print("\nNo Missing Values Found")

Data Shape:
(40, 65)

Duplicate Values:
( 0 )

Data Types:
object     54
float64     7
int32       4
Name: count, dtype: int64

No Missing Values Found

pheno.head(5)

	f0	Subject	RestScan	MeanFD	NumFD_greater_than_020	rootMeanSquareFD	FDquartiletop14thFD	PercentFD_greater_than_020	MeanDVARS	MeanFD_Jenkinson	...	sess_1_rest_6_eyes	sess_1_anat_1	sess_1_which_anat	sess_2_rest_1	sess_2_rest_1_eyes	sess_2_rest_2	sess_2_rest_2_eyes	sess_2_anat_1	defacing_ok	defacing_notes
0	"21"	10042	"rest_1"	0.0559	0	0.2365	0.0922	0.0000	2.2915	1.0089	...	NA	"pass"	NA	NA	NA	NA	NA	NA	""	""
1	"19"	10064	"rest_1"	0.0623	0	0.2496	0.0926	0.0000	2.0866	0.9943	...	NA	"pass"	NA	NA	NA	NA	NA	NA	""	""
2	"22"	10128	"rest_1"	0.0689	0	0.2624	0.1132	0.0000	2.1422	1.2641	...	NA	"pass"	NA	NA	NA	NA	NA	NA	""	""
3	"20"	21019	"rest_1"	0.0575	0	0.2398	0.0955	0.0000	2.0339	1.1973	...	NA	"pass"	NA	NA	NA	NA	NA	NA	"yes"	""
4	"30"	23008	"rest_1"	0.0801	7	0.2831	0.1710	8.9744	13.4263	1.7741	...	NA	"pass"	NA	NA	NA	NA	NA	NA	"yes"	""

5 rows × 65 columns

pheno[['tdc','adhd','age','sex']].head(10)

	tdc	adhd	age	sex
0	0	1	10.65	"M"
1	0	1	15.90	"M"
2	1	0	9.53	"M"
3	1	0	15.53	"M"
4	1	0	9.17	"M"
5	0	1	11.33	"F"
6	0	1	20.82	"M"
7	0	1	19.08	"M"
8	0	1	13.35	"M"
9	0	1	17.74	"M"

print('Number of classes:',pheno['sex'].value_counts())

Number of classes: sex
"M"    35
"F"     5
Name: count, dtype: int64

y = pheno['adhd']

print('Number of classes:',y.unique())

sns.set_style("white")
sns.set_palette("muted")
sns.countplot(x= y)

print(y.value_counts())

Number of classes: [1 0]
adhd
1    20
0    20
Name: count, dtype: int64

AGE DISTRIBUTION

age = pheno['age']

age.describe()

count    40.000000
mean     12.503586
std       3.373002
min       8.580000
25%       9.830000
50%      11.330000
75%      14.580000
max      20.820000
Name: age, dtype: float64

sns.set_style("dark")
sns.set_palette("dark")
sns.histplot(age)

#skewness and kurtosis
print("Asymmetry: %f" % y.skew())
print("Kurtosis: %f" % y.kurt())

Skewness: 0.000000
Kurtosis: -2.108108

The provided values represent the skewness and kurtosis of the 'age' column in the ADHD dataset.

• Skewness:

  • Skewness measures the asymmetry of the distribution of values in a dataset.
  • A skewness of 0 indicates a symmetric distribution.
  • In this case, the skewness value of 0.000000 suggests that the distribution of ages is approximately symmetric.

• Kurtosis:

  • Kurtosis measures the "tailedness" or the degree of outliers in the distribution of values.
  • A negative kurtosis indicates a platykurtic distribution, meaning the distribution has thinner tails and fewer outliers compared to a normal distribution.
  • The kurtosis value of -2.108108 suggests a platykurtic distribution for the ages in this dataset, indicating fewer outliers compared to a normal distribution.

Load the atlas

• The DiFuMo atlas provides dictionaries of functional modes optimized for extracting functional signals from fMRI data, available in various dimensionalities (64, 128, 256, 512, and 1024).

• Has multiple resolutions, for larger networks or finer-grained ROIs.

Let's use a 64-ROI atlas to allow some detail, but to ultimately keep our connectivity matrices manageable

dim = 64
difumo = datasets.fetch_atlas_difumo(
    dimension=dim, resolution_mm=2, legacy_format=False
)

atlas_filename = difumo.maps

This code segment loads the DiFuMo atlas, which provides dictionaries of functional modes optimized for extracting functional signals from fMRI data.

1. Specifying Atlas Dimensionality:

   • This line sets the desired dimensionality of the atlas to 64. This means the atlas will contain 64 regions of interest (ROIs).

2. Fetching the Atlas:

   • This line fetches the DiFuMo atlas using the fetch_atlas_difumo function from the datasets module in the nilearn library.
   • Parameters:
     • dimension=dim: Specifies the desired dimensionality of the atlas.
     • resolution_mm=2: Sets the resolution of the atlas in millimeters. Here, it's set to 2 mm.
     • legacy_format=False: This parameter is set to False, indicating that the fetched atlas will use the non-legacy format.

3. Accessing Atlas Filename:

   • This line extracts the filename of the atlas maps from the fetched difumo object.

After executing this code, the variable atlas_filename will contain the filename of the DiFuMo atlas maps corresponding to the specified dimensionality (64 ROIs) and resolution.

difumo.labels

	component	difumo_names	yeo_networks7	yeo_networks17	gm	wm	csf
0	1	Superior frontal sulcus	DefaultB	DefaultA	0.689996	0.185709	0.116884
1	2	Fusiform gyrus	No network found	No network found	0.844733	0.021026	0.133789
2	3	Calcarine cortex posterior	VisCent	VisPeri	0.601768	0.302067	0.091297
3	4	Cingulate cortex posterior	DefaultB	DefaultA	0.740086	0.140368	0.119567
4	5	Parieto-occipital sulcus superior	ContA	ContC	0.640157	0.241492	0.117826
...	...	...	...	...	...	...	...
59	60	Cuneus	VisCent	VisPeri	0.627179	0.269783	0.103005
60	61	Middle temporal gyrus	DefaultB	DefaultB	0.726527	0.149595	0.107329
61	62	Superior frontal gyrus	DefaultB	DefaultB	0.651182	0.062243	0.224067
62	63	Central sulcus	SomMotA	SomMotB	0.578502	0.291674	0.109244
63	64	Caudate	No network found	No network found	0.703295	0.260386	0.036332

64 rows × 7 columns

The provided data contains information about the labels of the regions in the DiFuMo atlas.

• Columns:

  • component: Represents the index or identifier of each region in the atlas.
  • difumo_names: Provides the name of the region according to the DiFuMo atlas.
  • yeo_networks7: Indicates the Yeo 7-network assignment for the region.
  • yeo_networks17: Indicates the Yeo 17-network assignment for the region.
  • gm: Represents the gray matter probability for the region.
  • wm: Represents the white matter probability for the region.
  • csf: Represents the cerebrospinal fluid probability for the region.

• Rows:

  • Each row corresponds to a specific region in the atlas, indexed by the component column.

• Data:

  • The data provides information about the anatomical and network assignments of each region, as well as probabilities of gray matter, white matter, and cerebrospinal fluid for each region.

This information is useful for understanding the anatomical and functional properties associated with each region in the DiFuMo atlas, which can be utilized in various neuroimaging analyses and interpretations.

Extract features with nilearn masker

Compute a correlation matrix, representing regional coactivation between regions and extract signals from a brain parcellation

from nilearn.maskers import MultiNiftiMapsMasker
from nilearn.connectome import ConnectivityMeasure

# create masker using MultiNiftiMapsMasker to extract functional data within
# atlas parcels from multiple subjects using parallelization to speed up the
# # computation
masker = MultiNiftiMapsMasker(
    maps_img=atlas_filename,
    standardize="zscore_sample",
    standardize_confounds="zscore_sample",
    memory="nilearn_cache",
    n_jobs=2, verbose=0
)

# ConenctivityMeasure from Nilearn uses simple 'correlation' to compute
# connectivity matrices for all subjects in a list
connectome_measure = ConnectivityMeasure(
    kind="correlation", vectorize=True, discard_diagonal=True)

Extract fMRI connectivity features from every subject.

all_features = [
    correlation_measure.fit_transform([masker.fit_transform(sub, confounds=data.confounds[i])])[0]
    for i, sub in enumerate(data.func)
]

1. Extracting fMRI Connectivity Features:

   • We want to analyze the functional MRI (fMRI) data from each subject to understand how different brain regions are connected or related.
   • To do this, we use the correlation_measure object we created earlier. This object knows how to compute correlation matrices, which show the strength of connections between brain regions.
   • We also use the masker object we set up to extract data from specific brain regions defined in the atlas.
   • The fit_transform method of the masker object takes the fMRI data from each subject (sub) and extracts information from the brain regions defined in the atlas. We also provide confound data to control for any factors that might influence the results.
   • Then, we pass this extracted data to the correlation_measure object's fit_transform method to compute the correlation matrices.
   • This process is repeated for each subject in the dataset (data.func), and the resulting correlation matrices are stored in the all_features list.

2. Understanding the Code:

   • enumerate(data.func): This iterates over the functional MRI data for each subject (sub) in the dataset, providing both the index (i) and the data itself.
   • correlation_measure.fit_transform(...): This computes the correlation matrices for the extracted data.
   • [0] at the end of the list comprehension: This is just accessing the first (and only) element in the list returned by fit_transform, as we're only interested in the correlation matrices.

In summary, we're using the masker and correlation_measure objects to process the fMRI data from each subject, extract connectivity features, and compute correlation matrices to understand how different brain regions are connected. These correlation matrices are then stored in the all_features list for further analysis.

# METHOD 2

# extract time series from all subjects
#time_series = masker.fit_transform(data_adhd, confounds=data_confounds)

# calculate correlation matrices across subjects and display
#correlation_matrices = connectome_measure.fit_transform(time_series)

# Let's save the data to disk

np.savez_compressed('ADHD_Difumo_features.npz',a = all_features)

# Load the features

feat_file = 'ADHD_Difumo_features.npz'
X_features = np.load(feat_file)['a']

print('Features shape:', X_features.shape)

Features shape: (40, 2016)

The 2016 features represent matrices of correlations.

1. Number of Subjects:

   • We have data for 40 subjects, as indicated by the first dimension of the shape (40, 2016).

2. Number of Features:

   • Each subject has a set of features associated with it.
   • In this case, each subject's features consist of a correlation matrix.
   • The correlation matrix represents the strength of connections between different brain regions.
   • Since each correlation matrix has been vectorized (flattened into a one-dimensional array) using the vectorize=True parameter when computing connectivity measures, each matrix is represented by 2016 features.
   • This number is derived from the fact that a symmetric matrix with 64 rows/columns (as in the case of the 64-ROI atlas used) would have ( \frac{{64 \times (64 + 1)}}{2} = 2016 ) unique elements after being vectorized, as it includes the diagonal elements.

So, each of the 2016 features corresponds to a specific connection between two brain regions in the correlation matrix. Each subject's set of features contains information about how strongly these connections are correlated.

# Create the plot
plt.figure(figsize=(6, 4))
plt.imshow(X_features, aspect='auto', cmap='Pastel2', interpolation='nearest')

# Add colorbar
plt.colorbar(label='Correlation')

# Add title and labels
plt.title('Feature Matrix', fontsize=14)
plt.xlabel('Features', fontsize=12)
plt.ylabel('Subjects', fontsize=12)

# Show the plot
plt.tight_layout()
plt.show()

Prepare data for machine learning

y_adhd = pheno['adhd']

print('y type:',type(y_adhd))
print('X type:',type(X_features))

y type: <class 'pandas.core.series.Series'>
X type: <class 'numpy.ndarray'>

from sklearn.model_selection import train_test_split

# Split the sample into training/test, stratify by age class, and shuffle the data
X_train, X_test, y_train, y_test = train_test_split(
    X_features,  # X 
    y_adhd,  # y 
    test_size=0.2,  # 80%/20% split
    shuffle=True,  # shuffle dataset before splitting
    stratify=y,  # keep distribution of ageclass consistent between train & test sets.
    random_state=123  # same shuffle each time
)

# Print the size of the training and test sets
print('training:', len(X_train), 'testing:', len(X_test))

training: 24 testing: 16

This code snippet utilizes the train_test_split function from scikit-learn to split the dataset into training and testing sets for machine learning:

1. Splitting the Data:

   • train_test_split divides the dataset into training and testing subsets.
   • X_features represents the feature matrix containing the correlation features, and y_adhd is the target variable indicating ADHD diagnosis.
   • test_size=0.2 specifies that 20% of the data will be used for testing, while 80% will be used for training.
   • shuffle=True ensures that the data is shuffled before splitting to prevent any potential biases in the dataset.
   • stratify=y_adhd ensures that the distribution of ADHD diagnosis classes is maintained in both the training and testing sets. This is important for ensuring representative samples in each subset.
   • random_state=123 sets the seed for random number generation, ensuring reproducibility of the split.

2. Printing Sizes of Sets:

   • The sizes of the training and testing sets are printed using len(X_train) and len(X_test) respectively.

This process ensures that we have separate datasets for training and testing our machine learning models, with appropriate proportions and balanced class distributions.

# Check data distribution
sns.histplot(y_train, label='train', kde=True)
sns.histplot(y_test, label='test', kde=True)
plt.legend()
plt.xlabel('Value')
plt.ylabel('Frequency')
plt.title('Distribution of Target Variable')
plt.show()

# Print the size of the training and test sets
print('training:', len(X_train), 'testing:', len(X_test))

Run our model!

We'll start with a standard classification model called a Support Vector Classifier (SVC)

Despite its simplicity, this model shines in its ability to deliver robust results. Given our data constraints, a straightforward approach often proves to be the most effective.

from sklearn.svm import SVC
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.metrics import accuracy_score, classification_report

# Create an instance of the Support Vector Classifier
svc_model = SVC()

# Define hyperparameters to tune
param_grid = {
    'C': [0.1, 1, 10],  # Penalty parameter C
    'kernel': ['linear'],  # Kernel type to be used in the algorithm
    'gamma': ['scale', 'auto']  # Kernel coefficient for 'rbf', 'poly', and 'sigmoid'
}

# Perform grid search cross-validation
grid_search = GridSearchCV(estimator=svc_model, param_grid=param_grid, cv=5)
grid_search.fit(X_train, y_train)

# Get the best parameters
best_params = grid_search.best_params_

This code runs a Support Vector Classifier (SVC) model and performs hyperparameter tuning using grid search cross-validation:

1. Creating the SVC Model:

   • An instance of the Support Vector Classifier (SVC) is created with the default hyperparameters.

2. Defining Hyperparameters to Tune:

   • Hyperparameters are parameters that are not directly learned by the model during training but affect the learning process. In this case, we're tuning the following hyperparameters:
     • C: Penalty parameter C, which controls the trade-off between a smooth decision boundary and correctly classifying training points.
     • kernel: The kernel type to be used in the algorithm. Here, we're using a linear kernel.
     • gamma: The kernel coefficient for certain kernel types. For a linear kernel, this parameter is ignored.

3. Performing Grid Search Cross-Validation:

   • Grid search cross-validation is used to find the best combination of hyperparameters.
   • It systematically evaluates different combinations of hyperparameters using cross-validation to determine which combination yields the best performance.
   • The cv parameter specifies the number of folds for cross-validation, which is set to 5 here.

4. Getting the Best Parameters:

   • After grid search is complete, the best combination of hyperparameters is obtained using grid_search.best_params_.

Overall, this code efficiently tunes the hyperparameters of the SVC model to optimize its performance on the training data.

# Train the model with the best parameters
best_svc_model = SVC(**best_params)
best_svc_model.fit(X_train, y_train)

# Make predictions on the test data
y_pred = best_svc_model.predict(X_test)

# Evaluate model performance
accuracy = accuracy_score(y_test, y_pred)
classification_rep = classification_report(y_test, y_pred)

# Print results
print("Best Parameters:", best_params)
print("Accuracy:", accuracy)
print("Classification Report:\n", classification_rep)

Best Parameters: {'C': 0.1, 'gamma': 'scale', 'kernel': 'linear'}
Accuracy: 0.5
Classification Report:
               precision    recall  f1-score   support

           0       0.50      0.25      0.33         8
           1       0.50      0.75      0.60         8

    accuracy                           0.50        16
   macro avg       0.50      0.50      0.47        16
weighted avg       0.50      0.50      0.47        16

Classification report:

• Precision: How precise the model's positive predictions are.
• Recall: How many actual positives the model can identify.
• F1-score: A balance between precision and recall.
• Support: The number of instances for each class.
• Accuracy: Overall correctness of the model's predictions.

Support Vector Classifier (SVC) model with the best parameters obtained from grid search cross-validation, makes predictions on the test data, and evaluates the model's performance:

1. Training the Model with Best Parameters:

   • We create an instance of the SVC model (best_svc_model) using the best parameters obtained from grid search cross-validation.
   • The SVC class from scikit-learn is used, and we pass the best parameters (**best_params) to initialize the model.
   • We then fit the model to the training data (X_train and y_train) using the fit method.

2. Making Predictions:

   • After training the model, we use it to make predictions on the test data (X_test) using the predict method.
   • The predicted labels are stored in the variable y_pred.

3. Evaluating Model Performance:

   • We compute the accuracy of the model by comparing the predicted labels (y_pred) with the true labels (y_test) using the accuracy_score function.
   • Additionally, we generate a classification report using the classification_report function, which provides metrics such as precision, recall, and F1-score for each class.
   • The accuracy and classification report are printed to assess the model's performance on the test data.

The output shows the best parameters obtained from grid search cross-validation, the accuracy of the model on the test data, and the classification report containing performance metrics for each class (0 and 1) as well as aggregated metrics. In this example, the accuracy is 0.5, indicating moderate performance.

# Compute and plot the confusion matrix
from sklearn.metrics import confusion_matrix

conf_matrix = confusion_matrix(y_test, y_pred)

# Plot a prettier confusion matrix
plt.figure(figsize=(8, 6))
sns.set(font_scale=1.2)  # Adjust font size for labels
sns.heatmap(
    conf_matrix,
    annot=True,
    fmt="d",
    cmap="Blues",
    cbar=False,
    square=True,
    xticklabels=['CONTROL', 'ADHD'],
    yticklabels=['CONTROL', 'ADHD'],
)
plt.xlabel("Predicted", fontsize=12)
plt.ylabel("True", fontsize=12)
plt.title("", fontsize=15)
plt.show()

Interpretation of the classification report:

• Control:

  • Precision: 0.50
    • 50% of the instances predicted as control were actually control.
  • Recall: 0.25
    • 25% of the actual Control instances were correctly identified by the model.
  • F1-score: 0.33
    • This metric combines both precision and recall into a single value.
  • Support: 8
    • There are 8 instances of control in the test dataset.

• ADHD:

  • Precision: 0.50
    • 50% of the instances predicted as ADHD were actually ADHD.
  • Recall: 0.75
    • 75% of the actual ADHD instances were correctly identified by the model.
    • The model did a better job of capturing ADHD instances compared to control.
  • F1-score: 0.60
    • This indicates a better balance between precision and recall compared to control.
  • Support: 8
    • There are also 8 instances of ADHD in the test dataset.

Interpreting model feature importance

correlation_measure.inverse_transform(best_svc_model.coef_).shape

(1, 64, 64)

1. Interpreting Model Feature Importance:

   • We're trying to understand which brain regions (features) are most important for predicting ADHD using the SVM model.
   • To do this, we look at the coefficients (weights) assigned to each feature by the SVM model.

2. Coefficient Shape:

   • After processing, we have a set of coefficients, each corresponding to a pair of brain regions.
   • The shape of these coefficients is (1, 64, 64), which means we have one set of coefficients for each pair of brain regions.

3. Plotting Feature Importance:

   • We visualize these coefficients using a bar plot.
   • Each bar represents the weight assigned to a specific pair of brain regions by the SVM model.
   • The x-axis shows the brain regions (features), and the y-axis shows the weights.
   • We set the background color of the plot to dark blue for better visibility.

Essentially, this plot helps us understand which brain regions have the most influence on predicting ADHD based on their correlations. Each bar's height represents how important that specific brain region is in making accurate predictions.

# Get the coefficients (weights) of the linear SVM model from best_estimator
coefficients = best_svc_model.coef_



plt.bar(range(coefficients.shape[-1]),coefficients[0])
plt.gca().set_facecolor('darkblue')  # Change background color
plt.title('feature importances')
plt.xlabel('feature')
plt.ylabel('weight')

Text(0, 0.5, 'weight')

1. Interpreting Model Feature Importance:

   • This line of code aims to interpret the feature importance of the SVM model.
   • correlation_measure.inverse_transform(best_svc_model.coef_) is a function call that helps transform the coefficients of the SVM model back to the original space of the features.
   • The result of this transformation is stored in the variable feat_exp_matrix.

2. Understanding the Result:

   • feat_exp_matrix represents the feature importance matrix obtained from the SVM model.
   • Each element in feat_exp_matrix corresponds to the importance or weight assigned to a specific feature (in this case, the correlation between different brain regions).
   • The shape of feat_exp_matrix is (64, 64), indicating that it is a square matrix where each row and column correspond to one of the 64 brain regions.

feat_exp_matrix = correlation_measure.inverse_transform(best_svc_model.coef_)[0]

# Define a threshold to visualize only higher values
threshold = 0.05  # Adjust this threshold as needed

labels = difumo.labels["difumo_names"]

# Replace diagonal with NaN to remove it from the plot
np.fill_diagonal(feat_exp_matrix, np.nan)

# Plot the matrix
plt.figure(figsize=(20, 18))  # Adjust the figure size as needed
plt.imshow(feat_exp_matrix, cmap='viridis', origin='upper', vmin=threshold)
plt.colorbar(label='Correlation Strength', fraction=0.046, pad=0.04)  # Adjust color bar position

# Add labels to the ticks
plt.xticks(ticks=range(len(labels)), labels=labels, rotation=90)
plt.yticks(ticks=range(len(labels)), labels=labels)

# Add title
plt.title('Connectivity Matrix')

# Show the plot
plt.tight_layout()  # Adjust layout to prevent overlap
plt.show()

This code iterates over the correlation matrix and prints the correlation values between different brain regions that exceed the specified threshold.

1. Iteration Over the Matrix:

   • The code uses nested loops to iterate over each element of the correlation matrix.
   • The outer loop (for i in range(len(labels))) iterates over the rows of the matrix, representing one brain region.
   • The inner loop (for j in range(len(labels))) iterates over the columns of the matrix, representing another brain region.

2. Condition for Printing:

   • Within the nested loops, the code checks if the current element is not on the diagonal (i.e., i != j) to avoid printing self-correlations.
   • It also checks if the correlation value (feat_exp_matrix[i, j]) is greater than or equal to the specified threshold.

3. Printing Correlation Values:

   • If both conditions are met, the code prints the names of the two brain regions (labels[i] and labels[j]) along with their correlation value.

# Iterate over the correlation matrix and print the values
for i in range(len(labels)):
    for j in range(len(labels)):
        if i != j and feat_exp_matrix[i, j] >= threshold:
            print(f"{labels[i]} - {labels[j]}: {feat_exp_matrix[i, j]}")

Superior frontal sulcus - Cingulate cortex posterior: 0.024572098783108988
Superior frontal sulcus - Anterior Cingulate Cortex: 0.021465588250447396
Fusiform gyrus - Insula antero-superior: 0.02396235930523669
Fusiform gyrus - ventricles: 0.02796524345460276
Fusiform gyrus - Precuneus superior: 0.03954051566003608
Fusiform gyrus - Anterior Cingulate Cortex: 0.045386443894684894
Fusiform gyrus - Inferior occipital gyrus: 0.0384588487547811
Fusiform gyrus - Superior rostral gyrus: 0.022349567484306575
Fusiform gyrus - Superior parietal lobule: 0.02233224840085746
Calcarine cortex posterior - Superior occipital gyrus: 0.020087867115944312
Calcarine cortex posterior - Planum polare: 0.02173601249891338
Calcarine cortex posterior - Anterior Cingulate Cortex: 0.023252548826835674
Calcarine cortex posterior - Inferior occipital gyrus: 0.03493064271441605
Calcarine cortex posterior - Postcentral gyrus inferior: 0.02340693154085293
Cingulate cortex posterior - Superior frontal sulcus: 0.024572098783108988
Cingulate cortex posterior - Insula antero-superior: 0.05058447817292083
Cingulate cortex posterior - Planum temporale: 0.02355296976070756
Cingulate cortex posterior - Cerebellum Crus II: 0.022177604284786823
Cingulate cortex posterior - Superior parts of Postcentral and Precentral gyri: 0.03064682538331201
Cingulate cortex posterior - Paracentral gyrus RH: 0.021084718617357733
Cingulate cortex posterior - Superior frontal gyrus medial: 0.026068121887529237
Cingulate cortex posterior - Precuneus superior: 0.02419459431626161
Cingulate cortex posterior - Cerebellum I-V: 0.020881204198076604
Cingulate cortex posterior - Anterior Cingulate Cortex: 0.062397011665541194
Cingulate cortex posterior - Cingulate gyrus mid-anterior: 0.03326612481148376
Cingulate cortex posterior - Superior parietal lobule posterior: 0.03285212200674496
Cingulate cortex posterior - Supramarginal gyrus: 0.029963033278403193
Cingulate cortex posterior - Precentral gyrus superior: 0.049258771692586
Cingulate cortex posterior - Postcentral gyrus inferior: 0.024647388980006627
Cingulate cortex posterior - Callosomarginal sulcus: 0.0257537449593733
Cingulate cortex posterior - Heschl’s gyrus: 0.02391163019823206
Cingulate cortex posterior - Intraparietal sulcus RH: 0.028902029623437464
Cingulate cortex posterior - Postcentral gyrus LH: 0.02784968919469567
Cingulate cortex posterior - Middle frontal gyrus: 0.06502743674014841
Cingulate cortex posterior - Precuneus anterior: 0.022625033151112504
Cingulate cortex posterior - Superior parietal lobule: 0.03886337923618291
Cingulate cortex posterior - Middle frontal gyrus anterior: 0.04528895912600043
Cingulate cortex posterior - Superior frontal gyrus: 0.025950517569564447
Parieto-occipital sulcus superior - Cerebellum Crus II: 0.021070315387326524
Parieto-occipital sulcus superior - Angular gyrus superior: 0.030308742152800328
Parieto-occipital sulcus superior - Parieto-occipital sulcus anterior: 0.023607354548723716
Parieto-occipital sulcus superior - Angular gyrus inferior: 0.02703270776103122
Insula antero-superior - Fusiform gyrus: 0.02396235930523669
Insula antero-superior - Cingulate cortex posterior: 0.05058447817292083
Insula antero-superior - Superior temporal sulcus with angular gyrus: 0.02760037967197863
Insula antero-superior - Superior occipital gyrus: 0.03591984314088936
Insula antero-superior - Cingulate gyrus mid-posterior: 0.02933409216686269
Insula antero-superior - Fusiform gyrus posterior: 0.023183813976228033
Insula antero-superior - Precuneus superior: 0.024402257463852276
Insula antero-superior - Planum polare: 0.03672278915149496
Insula antero-superior - Parieto-occipital sulcus middle: 0.02301783148594108
Insula antero-superior - Descending occipital gyrus: 0.02196218059729364
Insula antero-superior - Dorsomedial prefrontal cortex antero-superior: 0.03131560902469789
Insula antero-superior - Heschl’s gyrus: 0.027731300877050884
Insula antero-superior - Occipital pole: 0.03623730667119611
Insula antero-superior - Parieto-occipital sulcus anterior: 0.03216019344374006
Superior temporal sulcus with angular gyrus - Insula antero-superior: 0.02760037967197863
Superior temporal sulcus with angular gyrus - Anterior Cingulate Cortex: 0.0765332938457802
Superior temporal sulcus with angular gyrus - Middle frontal gyrus anterior: 0.024385124449745502
Planum temporale - Cingulate cortex posterior: 0.02355296976070756
Planum temporale - Planum polare: 0.03234049345887994
Planum temporale - Anterior Cingulate Cortex: 0.027083248055962406
Planum temporale - Calcarine sulcus anterior: 0.02241501020202332
Planum temporale - Lingual gyrus anterior: 0.02238984639331046
Planum temporale - Callosomarginal sulcus: 0.03430052331003754
Planum temporale - Superior parietal lobule: 0.025535581662185586
Cerebellum Crus II - Cingulate cortex posterior: 0.022177604284786823
Cerebellum Crus II - Parieto-occipital sulcus superior: 0.021070315387326524
Cerebellum Crus II - Cingulate gyrus mid-posterior: 0.0277795058751471
Cerebellum Crus II - ventricles: 0.04576617978241995
Cerebellum Crus II - Precuneus superior: 0.05440219080449031
Cerebellum Crus II - Anterior Cingulate Cortex: 0.06602582572506618
Cerebellum Crus II - Superior parietal lobule posterior: 0.02334336375970296
Cerebellum Crus II - Superior rostral gyrus: 0.058192245755569534
Cerebellum Crus II - Intraparietal sulcus: 0.05054476853062033
Cerebellum Crus II - Angular gyrus superior: 0.02767980777222678
Cerebellum Crus II - Dorsomedial prefrontal cortex antero-superior: 0.049490324632080425
Cerebellum Crus II - Occipital pole: 0.02112125326645773
Cerebellum Crus II - Middle frontal gyrus: 0.023670459579349594
Cerebellum Crus II - Inferior frontal gyrus: 0.03419325331063984
Cerebellum Crus II - Superior parietal lobule: 0.033068794303003315
Cerebellum Crus II - Middle frontal gyrus anterior: 0.029828868717955405
Cerebellum Crus II - Angular gyrus inferior: 0.04835559921860546
Cerebellum Crus II - Superior frontal gyrus: 0.03335105687063897
Cerebellum Crus II - Caudate: 0.03953927947846987
Superior parts of Postcentral and Precentral gyri - Cingulate cortex posterior: 0.03064682538331201
Superior parts of Postcentral and Precentral gyri - ventricles: 0.023197163564488917
Superior parts of Postcentral and Precentral gyri - Anterior Cingulate Cortex: 0.02742860628072923
Superior parts of Postcentral and Precentral gyri - Superior rostral gyrus: 0.030987828242049074
Superior parts of Postcentral and Precentral gyri - Postcentral gyrus inferior: 0.03485450968865003
Superior parts of Postcentral and Precentral gyri - Angular gyrus inferior: 0.025535067838636967
Transverse sinus - ventricles: 0.05136524717836236
Transverse sinus - Precuneus superior: 0.03594439259141224
Transverse sinus - Anterior Cingulate Cortex: 0.036856913928931666
Transverse sinus - Superior parietal lobule posterior: 0.02171026291796746
Transverse sinus - Inferior occipital gyrus: 0.02839749217180095
Transverse sinus - Superior rostral gyrus: 0.022738215188974207
Transverse sinus - Middle frontal gyrus: 0.024399486958743388
Transverse sinus - Superior parietal lobule: 0.021766236572771817
Paracentral gyrus RH - Cingulate cortex posterior: 0.021084718617357733
Paracentral gyrus RH - Anterior Cingulate Cortex: 0.02908335971792618
Paracentral gyrus RH - Superior rostral gyrus: 0.0221831201574644
Paracentral gyrus RH - Postcentral gyrus inferior: 0.04293328887233179
Paracentral gyrus RH - Callosomarginal sulcus: 0.023974255436625347
Paracentral gyrus RH - Superior parietal lobule: 0.03029986418634357
Superior occipital gyrus - Calcarine cortex posterior: 0.020087867115944312
Superior occipital gyrus - Insula antero-superior: 0.03591984314088936
Superior occipital gyrus - ventricles: 0.049594188120890156
Superior occipital gyrus - Precuneus superior: 0.02606410094555466
Superior occipital gyrus - Planum polare: 0.038123891003711316
Superior occipital gyrus - Cingulate gyrus mid-anterior: 0.02039329830010903
Superior occipital gyrus - Inferior occipital gyrus: 0.0370633435660378
Superior occipital gyrus - Calcarine sulcus anterior: 0.027290789317706923
Superior occipital gyrus - Lingual gyrus anterior: 0.02792749186827548
Superior occipital gyrus - Supramarginal gyrus: 0.034661973147977275
Superior occipital gyrus - Intraparietal sulcus LH: 0.032770214482988586
Superior occipital gyrus - Postcentral gyrus inferior: 0.04086048533954996
Superior occipital gyrus - Intraparietal sulcus RH: 0.023097693628212367
Superior occipital gyrus - Precuneus anterior: 0.024401876794959258
Superior occipital gyrus - Superior parietal lobule: 0.021764185826580323
Superior occipital gyrus - Cuneus: 0.020790559620870244
Cingulate gyrus mid-posterior - Insula antero-superior: 0.02933409216686269
Cingulate gyrus mid-posterior - Cerebellum Crus II: 0.0277795058751471
Cingulate gyrus mid-posterior - Superior frontal gyrus medial: 0.02183343040878081
Cingulate gyrus mid-posterior - Precuneus superior: 0.020723692055098074
Cingulate gyrus mid-posterior - Anterior Cingulate Cortex: 0.04311061431294372
Cingulate gyrus mid-posterior - Superior parietal lobule posterior: 0.021309014001769187
Cingulate gyrus mid-posterior - Precentral gyrus superior: 0.0343959786470594
Cingulate gyrus mid-posterior - Middle frontal gyrus: 0.033213965474690396
Cingulate gyrus mid-posterior - Middle frontal gyrus anterior: 0.044352444266239924
ventricles - Fusiform gyrus: 0.02796524345460276
ventricles - Cerebellum Crus II: 0.04576617978241995
ventricles - Superior parts of Postcentral and Precentral gyri: 0.023197163564488917
ventricles - Transverse sinus: 0.05136524717836236
ventricles - Superior occipital gyrus: 0.049594188120890156
ventricles - Fusiform gyrus posterior: 0.03799163040473566
ventricles - Precuneus superior: 0.06600046961879227
ventricles - Descending occipital gyrus: 0.02608644504593679
ventricles - Superior parietal lobule posterior: 0.037001743729341195
ventricles - Superior rostral gyrus: 0.03535059522736483
ventricles - Supramarginal gyrus: 0.020440767154152134
ventricles - Dorsomedial prefrontal cortex antero-superior: 0.02858011598558558
ventricles - Precentral gyrus superior: 0.03446063137939254
ventricles - Lateral occipital cortex: 0.02911508843839884
ventricles - Occipital pole: 0.02573905875655913
ventricles - Inferior frontal sulcus: 0.023568025890305003
ventricles - Middle frontal gyrus: 0.031211786863893705
ventricles - Inferior frontal gyrus: 0.027911784553507814
ventricles - Superior occipital sulcus: 0.030669375547281743
ventricles - Superior parietal lobule: 0.04673274765279683
ventricles - Angular gyrus inferior: 0.02835752570660184
Fusiform gyrus posterior - Insula antero-superior: 0.023183813976228033
Fusiform gyrus posterior - ventricles: 0.03799163040473566
Fusiform gyrus posterior - Planum polare: 0.024169757207942972
Fusiform gyrus posterior - Anterior Cingulate Cortex: 0.04679415991875026
Fusiform gyrus posterior - Superior parietal lobule posterior: 0.02551258444126279
Fusiform gyrus posterior - Intraparietal sulcus: 0.02350877667497858
Fusiform gyrus posterior - Intraparietal sulcus LH: 0.034994072803199765
Fusiform gyrus posterior - Postcentral gyrus inferior: 0.02981608001737897
Fusiform gyrus posterior - Intraparietal sulcus RH: 0.038477932332586055
Fusiform gyrus posterior - Middle frontal gyrus: 0.028814124875484674
Fusiform gyrus posterior - Inferior frontal gyrus: 0.02195607184723937
Fusiform gyrus posterior - Superior parietal lobule: 0.034582976855749806
Superior frontal gyrus medial - Cingulate cortex posterior: 0.026068121887529237
Superior frontal gyrus medial - Cingulate gyrus mid-posterior: 0.02183343040878081
Superior frontal gyrus medial - Superior rostral gyrus: 0.026662241041122196
Superior frontal gyrus medial - Occipital pole: 0.024023702133437023
Superior frontal gyrus medial - Angular gyrus inferior: 0.03011896462801947
Precuneus superior - Fusiform gyrus: 0.03954051566003608
Precuneus superior - Cingulate cortex posterior: 0.02419459431626161
Precuneus superior - Insula antero-superior: 0.024402257463852276
Precuneus superior - Cerebellum Crus II: 0.05440219080449031
Precuneus superior - Transverse sinus: 0.03594439259141224
Precuneus superior - Superior occipital gyrus: 0.02606410094555466
Precuneus superior - Cingulate gyrus mid-posterior: 0.020723692055098074
Precuneus superior - ventricles: 0.06600046961879227
Precuneus superior - Planum polare: 0.03241718632461819
Precuneus superior - Cerebellum I-V: 0.03231158091746448
Precuneus superior - Anterior Cingulate Cortex: 0.03730893120149659
Precuneus superior - Descending occipital gyrus: 0.03788118417699235
Precuneus superior - Superior parietal lobule posterior: 0.03266142220828525
Precuneus superior - Intraparietal sulcus: 0.031236195151297594
Precuneus superior - Lingual gyrus anterior: 0.02935282419780551
Precuneus superior - Angular gyrus superior: 0.028521117598547863
Precuneus superior - Intraparietal sulcus LH: 0.03827355441449212
Precuneus superior - Precentral gyrus superior: 0.04234080276140227
Precuneus superior - Postcentral gyrus inferior: 0.0355309906623379
Precuneus superior - Lateral occipital cortex: 0.028672031130020727
Precuneus superior - Thalamus: 0.030030480813967197
Precuneus superior - Intraparietal sulcus RH: 0.046684946546806334
Precuneus superior - Inferior frontal sulcus: 0.0357672156024464
Precuneus superior - Middle frontal gyrus: 0.04456032588272195
Precuneus superior - Inferior frontal gyrus: 0.028461290740366612
Precuneus superior - Parieto-occipital sulcus anterior: 0.04806776964702013
Precuneus superior - Precuneus anterior: 0.02522333553558079
Precuneus superior - Lingual gyrus: 0.027303023633692226
Precuneus superior - Superior occipital sulcus: 0.04091763043551805
Precuneus superior - Superior parietal lobule: 0.02593231159069462
Precuneus superior - Central sulcus: 0.02569562202543034
Planum polare - Calcarine cortex posterior: 0.02173601249891338
Planum polare - Insula antero-superior: 0.03672278915149496
Planum polare - Planum temporale: 0.03234049345887994
Planum polare - Superior occipital gyrus: 0.038123891003711316
Planum polare - Fusiform gyrus posterior: 0.024169757207942972
Planum polare - Precuneus superior: 0.03241718632461819
Planum polare - Parieto-occipital sulcus middle: 0.027501497062733162
Planum polare - Descending occipital gyrus: 0.028782746028048225
Planum polare - Superior rostral gyrus: 0.023853519805432356
Planum polare - Calcarine sulcus anterior: 0.022077519520385832
Planum polare - Supramarginal gyrus: 0.03492145081009072
Planum polare - Dorsomedial prefrontal cortex antero-superior: 0.024011761625725228
Planum polare - Precentral gyrus superior: 0.021456947599495287
Planum polare - Lateral occipital cortex: 0.022350785947408126
Planum polare - Callosomarginal sulcus: 0.031697891866195156
Planum polare - Heschl’s gyrus: 0.02889142656799318
Planum polare - Occipital pole: 0.03305310738080194
Planum polare - Inferior frontal sulcus: 0.02148720265240705
Planum polare - Inferior frontal gyrus: 0.03373601911821551
Planum polare - Parieto-occipital sulcus anterior: 0.020937489640201805
Planum polare - Precuneus anterior: 0.024544242121798045
Planum polare - Superior parietal lobule: 0.027137660167613417
Parieto-occipital sulcus middle - Insula antero-superior: 0.02301783148594108
Parieto-occipital sulcus middle - Planum polare: 0.027501497062733162
Parieto-occipital sulcus middle - Supramarginal gyrus: 0.03296396068338635
Parieto-occipital sulcus middle - Postcentral gyrus inferior: 0.03559173319639446
Cerebellum I-V - Cingulate cortex posterior: 0.020881204198076604
Cerebellum I-V - Precuneus superior: 0.03231158091746448
Cerebellum I-V - Anterior Cingulate Cortex: 0.05174277875696272
Cerebellum I-V - Superior rostral gyrus: 0.025607445238538553
Cerebellum I-V - Supramarginal gyrus: 0.03169887527326673
Cerebellum I-V - Dorsomedial prefrontal cortex antero-superior: 0.03258635161218133
Cerebellum I-V - Postcentral gyrus inferior: 0.04066941987581136
Cerebellum I-V - Occipital pole: 0.025946388219448096
Cerebellum I-V - Inferior frontal gyrus: 0.041376799196504735
Cerebellum I-V - Superior parietal lobule: 0.02367009856418632
Cerebellum I-V - Angular gyrus inferior: 0.03188264567912002
Cerebellum I-V - Superior frontal gyrus: 0.0419723378386445
Anterior Cingulate Cortex - Superior frontal sulcus: 0.021465588250447396
Anterior Cingulate Cortex - Fusiform gyrus: 0.045386443894684894
Anterior Cingulate Cortex - Calcarine cortex posterior: 0.023252548826835674
Anterior Cingulate Cortex - Cingulate cortex posterior: 0.062397011665541194
Anterior Cingulate Cortex - Superior temporal sulcus with angular gyrus: 0.0765332938457802
Anterior Cingulate Cortex - Planum temporale: 0.027083248055962406
Anterior Cingulate Cortex - Cerebellum Crus II: 0.06602582572506618
Anterior Cingulate Cortex - Superior parts of Postcentral and Precentral gyri: 0.02742860628072923
Anterior Cingulate Cortex - Transverse sinus: 0.036856913928931666
Anterior Cingulate Cortex - Paracentral gyrus RH: 0.02908335971792618
Anterior Cingulate Cortex - Cingulate gyrus mid-posterior: 0.04311061431294372
Anterior Cingulate Cortex - Fusiform gyrus posterior: 0.04679415991875026
Anterior Cingulate Cortex - Precuneus superior: 0.03730893120149659
Anterior Cingulate Cortex - Cerebellum I-V: 0.05174277875696272
Anterior Cingulate Cortex - Descending occipital gyrus: 0.02794777887501885
Anterior Cingulate Cortex - Putamen: 0.032483297915604004
Anterior Cingulate Cortex - Superior parietal lobule posterior: 0.02003721436021013
Anterior Cingulate Cortex - Superior rostral gyrus: 0.06935571526424762
Anterior Cingulate Cortex - Calcarine sulcus anterior: 0.03858006628516223
Anterior Cingulate Cortex - Intraparietal sulcus: 0.02378593437736036
Anterior Cingulate Cortex - Lingual gyrus anterior: 0.02686299645472237
Anterior Cingulate Cortex - Angular gyrus superior: 0.06006634323374711
Anterior Cingulate Cortex - Dorsomedial prefrontal cortex antero-superior: 0.06346270854892735
Anterior Cingulate Cortex - Postcentral gyrus inferior: 0.044146786388960774
Anterior Cingulate Cortex - Lateral occipital cortex: 0.05337059894066619
Anterior Cingulate Cortex - Paracentral lobule superior: 0.05227124004123872
Anterior Cingulate Cortex - Heschl’s gyrus: 0.05012577054887324
Anterior Cingulate Cortex - Occipital pole: 0.049824228078125914
Anterior Cingulate Cortex - Inferior frontal sulcus: 0.029356860355617548
Anterior Cingulate Cortex - Inferior frontal gyrus: 0.036849526221523085
Anterior Cingulate Cortex - Parieto-occipital sulcus anterior: 0.0344700761083543
Anterior Cingulate Cortex - Superior parietal lobule: 0.030819918149411804
Anterior Cingulate Cortex - Middle frontal gyrus anterior: 0.020839602458621254
Anterior Cingulate Cortex - Angular gyrus inferior: 0.09245993901160833
Anterior Cingulate Cortex - Superior frontal gyrus: 0.027084829406132466
Anterior Cingulate Cortex - Caudate: 0.02546249725542627
Descending occipital gyrus - Insula antero-superior: 0.02196218059729364
Descending occipital gyrus - ventricles: 0.02608644504593679
Descending occipital gyrus - Precuneus superior: 0.03788118417699235
Descending occipital gyrus - Planum polare: 0.028782746028048225
Descending occipital gyrus - Anterior Cingulate Cortex: 0.02794777887501885
Descending occipital gyrus - Inferior occipital gyrus: 0.030683360906194262
Descending occipital gyrus - Supramarginal gyrus: 0.0208093161520854
Descending occipital gyrus - Intraparietal sulcus LH: 0.03198468332317604
Descending occipital gyrus - Intraparietal sulcus RH: 0.033417645402016416
Descending occipital gyrus - Precuneus anterior: 0.0201287728997811
Descending occipital gyrus - Superior parietal lobule: 0.03178937889956278
Putamen - Anterior Cingulate Cortex: 0.032483297915604004
Cingulate gyrus mid-anterior - Cingulate cortex posterior: 0.03326612481148376
Cingulate gyrus mid-anterior - Superior occipital gyrus: 0.02039329830010903
Cingulate gyrus mid-anterior - Occipital pole: 0.02730893310825364
Cingulate gyrus mid-anterior - Parieto-occipital sulcus anterior: 0.02519604290220931
Cingulate gyrus mid-anterior - Angular gyrus inferior: 0.025079464470847954
Superior parietal lobule posterior - Cingulate cortex posterior: 0.03285212200674496
Superior parietal lobule posterior - Cerebellum Crus II: 0.02334336375970296
Superior parietal lobule posterior - Transverse sinus: 0.02171026291796746
Superior parietal lobule posterior - Cingulate gyrus mid-posterior: 0.021309014001769187
Superior parietal lobule posterior - ventricles: 0.037001743729341195
Superior parietal lobule posterior - Fusiform gyrus posterior: 0.02551258444126279
Superior parietal lobule posterior - Precuneus superior: 0.03266142220828525
Superior parietal lobule posterior - Anterior Cingulate Cortex: 0.02003721436021013
Superior parietal lobule posterior - Intraparietal sulcus: 0.02890525653245347
Superior parietal lobule posterior - Inferior frontal gyrus: 0.022761477621522593
Superior parietal lobule posterior - Parieto-occipital sulcus anterior: 0.030758432465090343
Superior parietal lobule posterior - Superior parietal lobule: 0.031198499932633444
Paracentral lobule - Postcentral gyrus inferior: 0.022150753790463378
Paracentral lobule - Paracentral lobule superior: 0.02518066338634169
Inferior occipital gyrus - Fusiform gyrus: 0.0384588487547811
Inferior occipital gyrus - Calcarine cortex posterior: 0.03493064271441605
Inferior occipital gyrus - Transverse sinus: 0.02839749217180095
Inferior occipital gyrus - Superior occipital gyrus: 0.0370633435660378
Inferior occipital gyrus - Descending occipital gyrus: 0.030683360906194262
Inferior occipital gyrus - Calcarine sulcus anterior: 0.03245751543553308
Inferior occipital gyrus - Lingual gyrus anterior: 0.02719952506913034
Inferior occipital gyrus - Intraparietal sulcus LH: 0.029856795546516175
Inferior occipital gyrus - Lateral occipital cortex: 0.024496396931818477
Inferior occipital gyrus - Lingual gyrus: 0.024646760884821664
Inferior occipital gyrus - Superior parietal lobule: 0.03112564712020063
Inferior occipital gyrus - Cuneus: 0.03705204225019097
Superior rostral gyrus - Fusiform gyrus: 0.022349567484306575
Superior rostral gyrus - Cerebellum Crus II: 0.058192245755569534
Superior rostral gyrus - Superior parts of Postcentral and Precentral gyri: 0.030987828242049074
Superior rostral gyrus - Transverse sinus: 0.022738215188974207
Superior rostral gyrus - Paracentral gyrus RH: 0.0221831201574644
Superior rostral gyrus - ventricles: 0.03535059522736483
Superior rostral gyrus - Superior frontal gyrus medial: 0.026662241041122196
Superior rostral gyrus - Planum polare: 0.023853519805432356
Superior rostral gyrus - Cerebellum I-V: 0.025607445238538553
Superior rostral gyrus - Anterior Cingulate Cortex: 0.06935571526424762
Superior rostral gyrus - Middle frontal gyrus anterior: 0.026227363518814092
Superior rostral gyrus - Caudate: 0.02797784006503763
Calcarine sulcus anterior - Planum temporale: 0.02241501020202332
Calcarine sulcus anterior - Superior occipital gyrus: 0.027290789317706923
Calcarine sulcus anterior - Planum polare: 0.022077519520385832
Calcarine sulcus anterior - Anterior Cingulate Cortex: 0.03858006628516223
Calcarine sulcus anterior - Inferior occipital gyrus: 0.03245751543553308
Calcarine sulcus anterior - Postcentral gyrus inferior: 0.021799474743033474
Intraparietal sulcus - Cerebellum Crus II: 0.05054476853062033
Intraparietal sulcus - Fusiform gyrus posterior: 0.02350877667497858
Intraparietal sulcus - Precuneus superior: 0.031236195151297594
Intraparietal sulcus - Anterior Cingulate Cortex: 0.02378593437736036
Intraparietal sulcus - Superior parietal lobule posterior: 0.02890525653245347
Superior parietal lobule anterior - Postcentral gyrus inferior: 0.03965938054801533
Superior parietal lobule anterior - Paracentral lobule superior: 0.03304688068384546
Lingual gyrus anterior - Planum temporale: 0.02238984639331046
Lingual gyrus anterior - Superior occipital gyrus: 0.02792749186827548
Lingual gyrus anterior - Precuneus superior: 0.02935282419780551
Lingual gyrus anterior - Anterior Cingulate Cortex: 0.02686299645472237
Lingual gyrus anterior - Inferior occipital gyrus: 0.02719952506913034
Lingual gyrus anterior - Supramarginal gyrus: 0.021145272760753193
Lingual gyrus anterior - Postcentral gyrus inferior: 0.036551362735338884
Lingual gyrus anterior - Inferior frontal gyrus: 0.020087610069037386
Lingual gyrus anterior - Superior parietal lobule: 0.02340072097978824
Angular gyrus superior - Parieto-occipital sulcus superior: 0.030308742152800328
Angular gyrus superior - Cerebellum Crus II: 0.02767980777222678
Angular gyrus superior - Precuneus superior: 0.028521117598547863
Angular gyrus superior - Anterior Cingulate Cortex: 0.06006634323374711
Angular gyrus superior - Paracentral lobule superior: 0.032054351366451884
Angular gyrus superior - Middle frontal gyrus anterior: 0.034351144989554855
Supramarginal gyrus - Cingulate cortex posterior: 0.029963033278403193
Supramarginal gyrus - Superior occipital gyrus: 0.034661973147977275
Supramarginal gyrus - ventricles: 0.020440767154152134
Supramarginal gyrus - Planum polare: 0.03492145081009072
Supramarginal gyrus - Parieto-occipital sulcus middle: 0.03296396068338635
Supramarginal gyrus - Cerebellum I-V: 0.03169887527326673
Supramarginal gyrus - Descending occipital gyrus: 0.0208093161520854
Supramarginal gyrus - Lingual gyrus anterior: 0.021145272760753193
Supramarginal gyrus - Postcentral gyrus inferior: 0.02073400950361869
Supramarginal gyrus - Occipital pole: 0.03036467959954299
Supramarginal gyrus - Parieto-occipital sulcus anterior: 0.026949615834814616
Supramarginal gyrus - Lingual gyrus: 0.02603890716149865
Supramarginal gyrus - Superior parietal lobule: 0.024296003008624077
Supramarginal gyrus - Central sulcus: 0.02396115759485133
Intraparietal sulcus LH - Superior occipital gyrus: 0.032770214482988586
Intraparietal sulcus LH - Fusiform gyrus posterior: 0.034994072803199765
Intraparietal sulcus LH - Precuneus superior: 0.03827355441449212
Intraparietal sulcus LH - Descending occipital gyrus: 0.03198468332317604
Intraparietal sulcus LH - Inferior occipital gyrus: 0.029856795546516175
Intraparietal sulcus LH - Parieto-occipital sulcus anterior: 0.020036336154243634
Intraparietal sulcus LH - Superior occipital sulcus: 0.03290728257114556
Intraparietal sulcus LH - Superior parietal lobule: 0.026011484081115966
Dorsomedial prefrontal cortex antero-superior - Insula antero-superior: 0.03131560902469789
Dorsomedial prefrontal cortex antero-superior - Cerebellum Crus II: 0.049490324632080425
Dorsomedial prefrontal cortex antero-superior - ventricles: 0.02858011598558558
Dorsomedial prefrontal cortex antero-superior - Planum polare: 0.024011761625725228
Dorsomedial prefrontal cortex antero-superior - Cerebellum I-V: 0.03258635161218133
Dorsomedial prefrontal cortex antero-superior - Anterior Cingulate Cortex: 0.06346270854892735
Dorsomedial prefrontal cortex antero-superior - Paracentral lobule superior: 0.023320696728599842
Dorsomedial prefrontal cortex antero-superior - Heschl’s gyrus: 0.02040101716401565
Dorsomedial prefrontal cortex antero-superior - Occipital pole: 0.02116885867737294
Dorsomedial prefrontal cortex antero-superior - Middle frontal gyrus: 0.0249890332954356
Dorsomedial prefrontal cortex antero-superior - Inferior frontal gyrus: 0.02173752749134353
Dorsomedial prefrontal cortex antero-superior - Middle frontal gyrus anterior: 0.03658093963152918
Dorsomedial prefrontal cortex antero-superior - Angular gyrus inferior: 0.029463169688333714
Precentral gyrus superior - Cingulate cortex posterior: 0.049258771692586
Precentral gyrus superior - Cingulate gyrus mid-posterior: 0.0343959786470594
Precentral gyrus superior - ventricles: 0.03446063137939254
Precentral gyrus superior - Precuneus superior: 0.04234080276140227
Precentral gyrus superior - Planum polare: 0.021456947599495287
Precentral gyrus superior - Intraparietal sulcus RH: 0.02795262295378409
Precentral gyrus superior - Parieto-occipital sulcus anterior: 0.035251581297930684
Precentral gyrus superior - Precuneus anterior: 0.025365419531118615
Postcentral gyrus inferior - Calcarine cortex posterior: 0.02340693154085293
Postcentral gyrus inferior - Cingulate cortex posterior: 0.024647388980006627
Postcentral gyrus inferior - Superior parts of Postcentral and Precentral gyri: 0.03485450968865003
Postcentral gyrus inferior - Paracentral gyrus RH: 0.04293328887233179
Postcentral gyrus inferior - Superior occipital gyrus: 0.04086048533954996
Postcentral gyrus inferior - Fusiform gyrus posterior: 0.02981608001737897
Postcentral gyrus inferior - Precuneus superior: 0.0355309906623379
Postcentral gyrus inferior - Parieto-occipital sulcus middle: 0.03559173319639446
Postcentral gyrus inferior - Cerebellum I-V: 0.04066941987581136
Postcentral gyrus inferior - Anterior Cingulate Cortex: 0.044146786388960774
Postcentral gyrus inferior - Paracentral lobule: 0.022150753790463378
Postcentral gyrus inferior - Calcarine sulcus anterior: 0.021799474743033474
Postcentral gyrus inferior - Superior parietal lobule anterior: 0.03965938054801533
Postcentral gyrus inferior - Lingual gyrus anterior: 0.036551362735338884
Postcentral gyrus inferior - Supramarginal gyrus: 0.02073400950361869
Postcentral gyrus inferior - Lateral occipital cortex: 0.03751686739724017
Postcentral gyrus inferior - Callosomarginal sulcus: 0.04948815192787895
Postcentral gyrus inferior - Paracentral lobule superior: 0.02253202493899083
Postcentral gyrus inferior - Heschl’s gyrus: 0.020592093459780844
Postcentral gyrus inferior - Occipital pole: 0.022539831661802442
Postcentral gyrus inferior - Postcentral gyrus LH: 0.02684323861047421
Postcentral gyrus inferior - Parieto-occipital sulcus anterior: 0.02298512217257711
Postcentral gyrus inferior - Precuneus anterior: 0.040395361774852485
Postcentral gyrus inferior - Lingual gyrus: 0.0273289776609743
Postcentral gyrus inferior - Superior parietal lobule: 0.035668245270909074
Lateral occipital cortex - ventricles: 0.02911508843839884
Lateral occipital cortex - Precuneus superior: 0.028672031130020727
Lateral occipital cortex - Planum polare: 0.022350785947408126
Lateral occipital cortex - Anterior Cingulate Cortex: 0.05337059894066619
Lateral occipital cortex - Inferior occipital gyrus: 0.024496396931818477
Lateral occipital cortex - Postcentral gyrus inferior: 0.03751686739724017
Lateral occipital cortex - Inferior frontal gyrus: 0.029438439311844932
Lateral occipital cortex - Superior parietal lobule: 0.030036046344906323
Callosomarginal sulcus - Cingulate cortex posterior: 0.0257537449593733
Callosomarginal sulcus - Planum temporale: 0.03430052331003754
Callosomarginal sulcus - Paracentral gyrus RH: 0.023974255436625347
Callosomarginal sulcus - Planum polare: 0.031697891866195156
Callosomarginal sulcus - Postcentral gyrus inferior: 0.04948815192787895
Callosomarginal sulcus - Heschl’s gyrus: 0.02537081234964843
Callosomarginal sulcus - Inferior frontal gyrus: 0.02090353579863594
Callosomarginal sulcus - Central sulcus: 0.02741210185858165
Paracentral lobule superior - Anterior Cingulate Cortex: 0.05227124004123872
Paracentral lobule superior - Paracentral lobule: 0.02518066338634169
Paracentral lobule superior - Superior parietal lobule anterior: 0.03304688068384546
Paracentral lobule superior - Angular gyrus superior: 0.032054351366451884
Paracentral lobule superior - Dorsomedial prefrontal cortex antero-superior: 0.023320696728599842
Paracentral lobule superior - Postcentral gyrus inferior: 0.02253202493899083
Paracentral lobule superior - Inferior frontal gyrus: 0.031733007971362456
Paracentral lobule superior - Angular gyrus inferior: 0.031878716530771456
Paracentral lobule superior - Superior frontal gyrus: 0.02789240584228514
Heschl’s gyrus - Cingulate cortex posterior: 0.02391163019823206
Heschl’s gyrus - Insula antero-superior: 0.027731300877050884
Heschl’s gyrus - Planum polare: 0.02889142656799318
Heschl’s gyrus - Anterior Cingulate Cortex: 0.05012577054887324
Heschl’s gyrus - Dorsomedial prefrontal cortex antero-superior: 0.02040101716401565
Heschl’s gyrus - Postcentral gyrus inferior: 0.020592093459780844
Heschl’s gyrus - Callosomarginal sulcus: 0.02537081234964843
Heschl’s gyrus - Occipital pole: 0.02093471800586097
Heschl’s gyrus - Superior parietal lobule: 0.028214433524183746
Occipital pole - Insula antero-superior: 0.03623730667119611
Occipital pole - Cerebellum Crus II: 0.02112125326645773
Occipital pole - ventricles: 0.02573905875655913
Occipital pole - Superior frontal gyrus medial: 0.024023702133437023
Occipital pole - Planum polare: 0.03305310738080194
Occipital pole - Cerebellum I-V: 0.025946388219448096
Occipital pole - Anterior Cingulate Cortex: 0.049824228078125914
Occipital pole - Cingulate gyrus mid-anterior: 0.02730893310825364
Occipital pole - Supramarginal gyrus: 0.03036467959954299
Occipital pole - Dorsomedial prefrontal cortex antero-superior: 0.02116885867737294
Occipital pole - Postcentral gyrus inferior: 0.022539831661802442
Occipital pole - Heschl’s gyrus: 0.02093471800586097
Occipital pole - Superior frontal gyrus: 0.02117279894618387
Thalamus - Precuneus superior: 0.030030480813967197
Thalamus - Inferior frontal gyrus: 0.020192605859804754
Thalamus - Superior parietal lobule: 0.02207833349067751
Intraparietal sulcus RH - Cingulate cortex posterior: 0.028902029623437464
Intraparietal sulcus RH - Superior occipital gyrus: 0.023097693628212367
Intraparietal sulcus RH - Fusiform gyrus posterior: 0.038477932332586055
Intraparietal sulcus RH - Precuneus superior: 0.046684946546806334
Intraparietal sulcus RH - Descending occipital gyrus: 0.033417645402016416
Intraparietal sulcus RH - Precentral gyrus superior: 0.02795262295378409
Intraparietal sulcus RH - Parieto-occipital sulcus anterior: 0.042722599653188795
Intraparietal sulcus RH - Precuneus anterior: 0.025936511307235764
Intraparietal sulcus RH - Superior occipital sulcus: 0.022252953139385707
Intraparietal sulcus RH - Superior parietal lobule: 0.022663290681155666
Inferior frontal sulcus - ventricles: 0.023568025890305003
Inferior frontal sulcus - Precuneus superior: 0.0357672156024464
Inferior frontal sulcus - Planum polare: 0.02148720265240705
Inferior frontal sulcus - Anterior Cingulate Cortex: 0.029356860355617548
Postcentral gyrus LH - Cingulate cortex posterior: 0.02784968919469567
Postcentral gyrus LH - Postcentral gyrus inferior: 0.02684323861047421
Postcentral gyrus LH - Superior parietal lobule: 0.030010498406140368
Middle frontal gyrus - Cingulate cortex posterior: 0.06502743674014841
Middle frontal gyrus - Cerebellum Crus II: 0.023670459579349594
Middle frontal gyrus - Transverse sinus: 0.024399486958743388
Middle frontal gyrus - Cingulate gyrus mid-posterior: 0.033213965474690396
Middle frontal gyrus - ventricles: 0.031211786863893705
Middle frontal gyrus - Fusiform gyrus posterior: 0.028814124875484674
Middle frontal gyrus - Precuneus superior: 0.04456032588272195
Middle frontal gyrus - Dorsomedial prefrontal cortex antero-superior: 0.0249890332954356
Middle frontal gyrus - Parieto-occipital sulcus anterior: 0.03989216578300447
Middle frontal gyrus - Precuneus anterior: 0.022173912317855936
Middle frontal gyrus - Angular gyrus inferior: 0.03560446296264776
Inferior frontal gyrus - Cerebellum Crus II: 0.03419325331063984
Inferior frontal gyrus - ventricles: 0.027911784553507814
Inferior frontal gyrus - Fusiform gyrus posterior: 0.02195607184723937
Inferior frontal gyrus - Precuneus superior: 0.028461290740366612
Inferior frontal gyrus - Planum polare: 0.03373601911821551
Inferior frontal gyrus - Cerebellum I-V: 0.041376799196504735
Inferior frontal gyrus - Anterior Cingulate Cortex: 0.036849526221523085
Inferior frontal gyrus - Superior parietal lobule posterior: 0.022761477621522593
Inferior frontal gyrus - Lingual gyrus anterior: 0.020087610069037386
Inferior frontal gyrus - Dorsomedial prefrontal cortex antero-superior: 0.02173752749134353
Inferior frontal gyrus - Lateral occipital cortex: 0.029438439311844932
Inferior frontal gyrus - Callosomarginal sulcus: 0.02090353579863594
Inferior frontal gyrus - Paracentral lobule superior: 0.031733007971362456
Inferior frontal gyrus - Thalamus: 0.020192605859804754
Inferior frontal gyrus - Superior parietal lobule: 0.020854332879218188
Inferior frontal gyrus - Middle frontal gyrus anterior: 0.024239411217934374
Inferior frontal gyrus - Caudate: 0.026291502318687574
Parieto-occipital sulcus anterior - Parieto-occipital sulcus superior: 0.023607354548723716
Parieto-occipital sulcus anterior - Insula antero-superior: 0.03216019344374006
Parieto-occipital sulcus anterior - Precuneus superior: 0.04806776964702013
Parieto-occipital sulcus anterior - Planum polare: 0.020937489640201805
Parieto-occipital sulcus anterior - Anterior Cingulate Cortex: 0.0344700761083543
Parieto-occipital sulcus anterior - Cingulate gyrus mid-anterior: 0.02519604290220931
Parieto-occipital sulcus anterior - Superior parietal lobule posterior: 0.030758432465090343
Parieto-occipital sulcus anterior - Supramarginal gyrus: 0.026949615834814616
Parieto-occipital sulcus anterior - Intraparietal sulcus LH: 0.020036336154243634
Parieto-occipital sulcus anterior - Precentral gyrus superior: 0.035251581297930684
Parieto-occipital sulcus anterior - Postcentral gyrus inferior: 0.02298512217257711
Parieto-occipital sulcus anterior - Intraparietal sulcus RH: 0.042722599653188795
Parieto-occipital sulcus anterior - Middle frontal gyrus: 0.03989216578300447
Parieto-occipital sulcus anterior - Precuneus anterior: 0.029060289390138185
Parieto-occipital sulcus anterior - Superior parietal lobule: 0.03138566574199083
Parieto-occipital sulcus anterior - Middle frontal gyrus anterior: 0.03060294897665207
Precuneus anterior - Cingulate cortex posterior: 0.022625033151112504
Precuneus anterior - Superior occipital gyrus: 0.024401876794959258
Precuneus anterior - Precuneus superior: 0.02522333553558079
Precuneus anterior - Planum polare: 0.024544242121798045
Precuneus anterior - Descending occipital gyrus: 0.0201287728997811
Precuneus anterior - Precentral gyrus superior: 0.025365419531118615
Precuneus anterior - Postcentral gyrus inferior: 0.040395361774852485
Precuneus anterior - Intraparietal sulcus RH: 0.025936511307235764
Precuneus anterior - Middle frontal gyrus: 0.022173912317855936
Precuneus anterior - Parieto-occipital sulcus anterior: 0.029060289390138185
Precuneus anterior - Superior parietal lobule: 0.03130809252407984
Precuneus anterior - Central sulcus: 0.027718512718858737
Lingual gyrus - Precuneus superior: 0.027303023633692226
Lingual gyrus - Inferior occipital gyrus: 0.024646760884821664
Lingual gyrus - Supramarginal gyrus: 0.02603890716149865
Lingual gyrus - Postcentral gyrus inferior: 0.0273289776609743
Superior occipital sulcus - ventricles: 0.030669375547281743
Superior occipital sulcus - Precuneus superior: 0.04091763043551805
Superior occipital sulcus - Intraparietal sulcus LH: 0.03290728257114556
Superior occipital sulcus - Intraparietal sulcus RH: 0.022252953139385707
Superior occipital sulcus - Superior parietal lobule: 0.037625220218815696
Superior parietal lobule - Fusiform gyrus: 0.02233224840085746
Superior parietal lobule - Cingulate cortex posterior: 0.03886337923618291
Superior parietal lobule - Planum temporale: 0.025535581662185586
Superior parietal lobule - Cerebellum Crus II: 0.033068794303003315
Superior parietal lobule - Transverse sinus: 0.021766236572771817
Superior parietal lobule - Paracentral gyrus RH: 0.03029986418634357
Superior parietal lobule - Superior occipital gyrus: 0.021764185826580323
Superior parietal lobule - ventricles: 0.04673274765279683
Superior parietal lobule - Fusiform gyrus posterior: 0.034582976855749806
Superior parietal lobule - Precuneus superior: 0.02593231159069462
Superior parietal lobule - Planum polare: 0.027137660167613417
Superior parietal lobule - Cerebellum I-V: 0.02367009856418632
Superior parietal lobule - Anterior Cingulate Cortex: 0.030819918149411804
Superior parietal lobule - Descending occipital gyrus: 0.03178937889956278
Superior parietal lobule - Superior parietal lobule posterior: 0.031198499932633444
Superior parietal lobule - Inferior occipital gyrus: 0.03112564712020063
Superior parietal lobule - Lingual gyrus anterior: 0.02340072097978824
Superior parietal lobule - Supramarginal gyrus: 0.024296003008624077
Superior parietal lobule - Intraparietal sulcus LH: 0.026011484081115966
Superior parietal lobule - Postcentral gyrus inferior: 0.035668245270909074
Superior parietal lobule - Lateral occipital cortex: 0.030036046344906323
Superior parietal lobule - Heschl’s gyrus: 0.028214433524183746
Superior parietal lobule - Thalamus: 0.02207833349067751
Superior parietal lobule - Intraparietal sulcus RH: 0.022663290681155666
Superior parietal lobule - Postcentral gyrus LH: 0.030010498406140368
Superior parietal lobule - Inferior frontal gyrus: 0.020854332879218188
Superior parietal lobule - Parieto-occipital sulcus anterior: 0.03138566574199083
Superior parietal lobule - Precuneus anterior: 0.03130809252407984
Superior parietal lobule - Superior occipital sulcus: 0.037625220218815696
Superior parietal lobule - Central sulcus: 0.024475610625438158
Middle frontal gyrus anterior - Cingulate cortex posterior: 0.04528895912600043
Middle frontal gyrus anterior - Superior temporal sulcus with angular gyrus: 0.024385124449745502
Middle frontal gyrus anterior - Cerebellum Crus II: 0.029828868717955405
Middle frontal gyrus anterior - Cingulate gyrus mid-posterior: 0.044352444266239924
Middle frontal gyrus anterior - Anterior Cingulate Cortex: 0.020839602458621254
Middle frontal gyrus anterior - Superior rostral gyrus: 0.026227363518814092
Middle frontal gyrus anterior - Angular gyrus superior: 0.034351144989554855
Middle frontal gyrus anterior - Dorsomedial prefrontal cortex antero-superior: 0.03658093963152918
Middle frontal gyrus anterior - Inferior frontal gyrus: 0.024239411217934374
Middle frontal gyrus anterior - Parieto-occipital sulcus anterior: 0.03060294897665207
Middle frontal gyrus anterior - Angular gyrus inferior: 0.047654154499829834
Middle frontal gyrus anterior - Superior frontal gyrus: 0.03203904814356154
Angular gyrus inferior - Parieto-occipital sulcus superior: 0.02703270776103122
Angular gyrus inferior - Cerebellum Crus II: 0.04835559921860546
Angular gyrus inferior - Superior parts of Postcentral and Precentral gyri: 0.025535067838636967
Angular gyrus inferior - ventricles: 0.02835752570660184
Angular gyrus inferior - Superior frontal gyrus medial: 0.03011896462801947
Angular gyrus inferior - Cerebellum I-V: 0.03188264567912002
Angular gyrus inferior - Anterior Cingulate Cortex: 0.09245993901160833
Angular gyrus inferior - Cingulate gyrus mid-anterior: 0.025079464470847954
Angular gyrus inferior - Dorsomedial prefrontal cortex antero-superior: 0.029463169688333714
Angular gyrus inferior - Paracentral lobule superior: 0.031878716530771456
Angular gyrus inferior - Middle frontal gyrus: 0.03560446296264776
Angular gyrus inferior - Middle frontal gyrus anterior: 0.047654154499829834
Angular gyrus inferior - Superior frontal gyrus: 0.030258537495194797
Angular gyrus inferior - Caudate: 0.028448207842517767
Cuneus - Superior occipital gyrus: 0.020790559620870244
Cuneus - Inferior occipital gyrus: 0.03705204225019097
Superior frontal gyrus - Cingulate cortex posterior: 0.025950517569564447
Superior frontal gyrus - Cerebellum Crus II: 0.03335105687063897
Superior frontal gyrus - Cerebellum I-V: 0.0419723378386445
Superior frontal gyrus - Anterior Cingulate Cortex: 0.027084829406132466
Superior frontal gyrus - Paracentral lobule superior: 0.02789240584228514
Superior frontal gyrus - Occipital pole: 0.02117279894618387
Superior frontal gyrus - Middle frontal gyrus anterior: 0.03203904814356154
Superior frontal gyrus - Angular gyrus inferior: 0.030258537495194797
Central sulcus - Precuneus superior: 0.02569562202543034
Central sulcus - Supramarginal gyrus: 0.02396115759485133
Central sulcus - Callosomarginal sulcus: 0.02741210185858165
Central sulcus - Precuneus anterior: 0.027718512718858737
Central sulcus - Superior parietal lobule: 0.024475610625438158
Caudate - Cerebellum Crus II: 0.03953927947846987
Caudate - Anterior Cingulate Cortex: 0.02546249725542627
Caudate - Superior rostral gyrus: 0.02797784006503763
Caudate - Inferior frontal gyrus: 0.026291502318687574
Caudate - Angular gyrus inferior: 0.028448207842517767

# grab center coordinates for probabilistic atlas
coordinates = plotting.find_probabilistic_atlas_cut_coords(
    maps_img=difumo.maps
)

# plot connectome with 85% edge strength in the connectivity
plotting.plot_connectome(
    feat_exp_matrix,
    coordinates,
    edge_threshold="85%",
    title=f"DiFuMo with {dim} dimensions (probabilistic)",
)
plotting.show()

1. Grabbing Center Coordinates for Probabilistic Atlas:

   • coordinates = plotting.find_probabilistic_atlas_cut_coords(maps_img=difumo.maps): This line of code uses the find_probabilistic_atlas_cut_coords() function from the plotting module in Nilearn to extract the center coordinates for the probabilistic atlas.
   • The maps_img=difumo.maps argument specifies the probabilistic atlas image from which the coordinates will be extracted.

2. Plotting the Connectome:

   • plotting.plot_connectome(): This function is used to visualize connectivity networks (connectomes) using brain surface plots or scatter plots.
   • Arguments:
     • feat_exp_matrix: The feature importance matrix or the connectivity matrix to be visualized.
     • coordinates: The coordinates of brain regions, typically obtained from the atlas used to parcellate the brain.
     • edge_threshold="85%": Specifies the threshold for displaying edges (connections) in the connectome. Here, "85%" means that only edges with strengths in the top 85% will be displayed.
     • title=f"DiFuMo with {dim} dimensions (probabilistic)": The title of the plot. It dynamically includes the dimensionality (dim) of the DiFuMo atlas used and specifies that it's a probabilistic atlas.

3. Displaying the Plot:

   • plotting.show(): This function displays the plot generated by the plot_connectome() function.

It highlights strong connections between brain regions while excluding weaker connections based on the specified threshold. The resulting plot provides insights into the organization of brain networks derived from the connectivity data.

# Create a connectome map where each node is an ROI

coords = plotting.find_probabilistic_atlas_cut_coords(
    maps_img=difumo.maps
)

plotting.plot_connectome(feat_exp_matrix, coords, colorbar=True, edge_threshold=0.035)

<nilearn.plotting.displays._projectors.OrthoProjector at 0x11b87b25d80>

plotting.view_connectome(feat_exp_matrix, coords, edge_threshold='98%',
                        edge_cmap='viridis')

threshold = 0.09  # Adjust this threshold as needed

# Iterate over the correlation matrix and print the values
for i in range(len(labels)):
    for j in range(len(labels)):
        if i != j and feat_exp_matrix[i, j] >= threshold:
            print(f"{labels[i]} - {labels[j]}: {feat_exp_matrix[i, j]}")

Anterior Cingulate Cortex - Angular gyrus inferior: 0.09245993901160833
Angular gyrus inferior - Anterior Cingulate Cortex: 0.09245993901160833

Anterior Cingulate Cortex (ACC) - Angular Gyrus Inferior (AGI):

• The correlation value is 0.09245993901160833.
• These two brain regions are known to be involved in different cognitive functions:
  • The Anterior Cingulate Cortex (ACC) is associated with various cognitive processes, including attention allocation, emotion regulation, and error detection.
  • The Angular Gyrus Inferior (AGI) is primarily involved in language processing, semantic cognition, and numerical processing.
• The positive correlation between ACC and AGI suggests that there is some degree of synchronized activity or connectivity between these regions during resting-state fMRI scans.
• In the context of ADHD, alterations in the connectivity between these regions may reflect disruptions in attentional control, cognitive processing, or other functions related to ADHD symptomatology.
• However, the correlation value is relatively low, indicating that the strength of connectivity between ACC and AGI is modest compared to other brain regions.

# Define a threshold to visualize only higher values
threshold = 0.09  # Adjust this threshold as needed

# Plot the matrix
plt.figure(figsize=(20, 18))  # Adjust the figure size as needed
plt.imshow(feat_exp_matrix, cmap='viridis', origin='upper', vmin=threshold)
plt.colorbar(label='Correlation Strength', fraction=0.046, pad=0.04)  # Adjust color bar position

# Add labels to the ticks
plt.xticks(ticks=range(len(labels)), labels=labels, rotation=90)
plt.yticks(ticks=range(len(labels)), labels=labels)

# Add title
plt.title('Connectivity Matrix')

# Show the plot
plt.tight_layout()  # Adjust layout to prevent overlap
plt.show()